

A133520


Smallest k such that p(n)^4 + k is prime where p(n) is the nth prime.


8



1, 2, 6, 10, 12, 10, 16, 16, 6, 12, 18, 16, 12, 28, 6, 22, 6, 16, 6, 16, 6, 16, 30, 6, 16, 42, 22, 42, 28, 52, 22, 16, 28, 10, 28, 70, 30, 42, 78, 36, 12, 42, 6, 12, 40, 12, 12, 16, 16, 16, 18, 10, 6, 22, 60, 46, 76, 46, 18, 126, 12, 22, 22, 6, 16, 16, 22, 18, 120, 22, 12, 6, 6, 36
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OFFSET

1,2


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


EXAMPLE

p(2)=3, 3^4 = 81; for odd k and n > 1, p(n)^r + k is even and thus not prime, so we only need consider even k.
for k = 2: 81 + 2 = 83, which is prime, so 2 is the smallest number that can be added to 81 to make a new prime.
Hence a(2) = 2.


MATHEMATICA

NextPrime[#]#&/@(Prime[Range[80]]^4) (* Harvey P. Dale, May 17 2015 *)


CROSSREFS

Cf. A030814, A054271, A091666, A133517, A133518, A133519, A133521, A133522, (A001223).
Sequence in context: A125241 A116043 A085258 * A099017 A298748 A139799
Adjacent sequences: A133517 A133518 A133519 * A133521 A133522 A133523


KEYWORD

easy,nonn


AUTHOR

Carl R. White, Sep 14 2007


STATUS

approved



